Sr Examen
Integral de (1/2)(((1-x)sqrt(1-2x+2x^2))+((x^2)ln(1-x+sqrt(1-2x-2x^2))-(x^2)lnx)) dx
Solución
Ha introducido
[src]
1 / | | ________________ / ________________\ | / 2 2 | / 2 | 2 | (1 - x)*\/ 1 - 2*x + 2*x + x *log\1 - x + \/ 1 - 2*x - 2*x / - x *log(x) | ----------------------------------------------------------------------------- dx | 2 | / 0
$$\int\limits_{0}^{1} \frac{\left(1 - x\right) \sqrt{2 x^{2} + \left(1 - 2 x\right)} + \left(- x^{2} \log{\left(x \right)} + x^{2} \log{\left(\left(1 - x\right) + \sqrt{- 2 x^{2} + \left(1 - 2 x\right)} \right)}\right)}{2}\, dx$$
Integral(((1 - x)*sqrt(1 - 2*x + 2*x^2) + x^2*log(1 - x + sqrt(1 - 2*x - 2*x^2)) - x^2*log(x))/2, (x, 0, 1))
Respuesta
[src]
1 1 1
/ / / 1
| | | /
| ________________ | / ________________ \ | ________________ |
| / 2 | 2 | / 2 | | / 2 | 2
| \/ 1 - 2*x + 2*x dx | x *log\1 + \/ 1 - 2*x - 2*x - x/ dx | -x*\/ 1 - 2*x + 2*x dx | -x *log(x) dx
| | | |
/ / / /
0 0 0 0
-------------------------- + ------------------------------------------ + ----------------------------- + -----------------
2 2 2 2
$$\frac{\int\limits_{0}^{1} \left(- x \sqrt{2 x^{2} - 2 x + 1}\right)\, dx}{2} + \frac{\int\limits_{0}^{1} \left(- x^{2} \log{\left(x \right)}\right)\, dx}{2} + \frac{\int\limits_{0}^{1} \sqrt{2 x^{2} - 2 x + 1}\, dx}{2} + \frac{\int\limits_{0}^{1} x^{2} \log{\left(- x + \sqrt{- 2 x^{2} - 2 x + 1} + 1 \right)}\, dx}{2}$$
=
=
1 1 1
/ / / 1
| | | /
| ________________ | / ________________ \ | ________________ |
| / 2 | 2 | / 2 | | / 2 | 2
| \/ 1 - 2*x + 2*x dx | x *log\1 + \/ 1 - 2*x - 2*x - x/ dx | -x*\/ 1 - 2*x + 2*x dx | -x *log(x) dx
| | | |
/ / / /
0 0 0 0
-------------------------- + ------------------------------------------ + ----------------------------- + -----------------
2 2 2 2
$$\frac{\int\limits_{0}^{1} \left(- x \sqrt{2 x^{2} - 2 x + 1}\right)\, dx}{2} + \frac{\int\limits_{0}^{1} \left(- x^{2} \log{\left(x \right)}\right)\, dx}{2} + \frac{\int\limits_{0}^{1} \sqrt{2 x^{2} - 2 x + 1}\, dx}{2} + \frac{\int\limits_{0}^{1} x^{2} \log{\left(- x + \sqrt{- 2 x^{2} - 2 x + 1} + 1 \right)}\, dx}{2}$$
Integral(sqrt(1 - 2*x + 2*x^2), (x, 0, 1))/2 + Integral(x^2*log(1 + sqrt(1 - 2*x - 2*x^2) - x), (x, 0, 1))/2 + Integral(-x*sqrt(1 - 2*x + 2*x^2), (x, 0, 1))/2 + Integral(-x^2*log(x), (x, 0, 1))/2
Respuesta numérica
[src]
(0.302291409149706 + 0.213469940850905j)
(0.302291409149706 + 0.213469940850905j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.